Choice & Inference

Observations are generally agreed to be laden with theory, and hence not entirely objective. It may be thought that if the data are objective anywhere, it is in statistics. In this paper I argue against this and reveal two ways in which statistical inference is affected by the theory-ladenness of observations. The first of these concerns well-known violations of the likelihood principle, namely in hypothesis testing and optional stopping. It appears that we can represent these violations as cases in which the likelihood principle is adhered to. But to achieve this, we have to accept that the content of the observations depends on the statistical hypotheses under consideration. Another way in which statistical data may be theory-laden concerns the influence of priors on how the observations affect our judgment over the hypotheses. I will discuss two cases in which the implicit or explicit adoption of a prior has specific implications for what is concluded from the observations, one in regression analysis and one in causal modelling. Rather than seeing these results in a negative light, as damaging to the objectivity of statistical methods, I think that they invite us to rethink the role of theory-ladenness. I argue that it is exactly because of the theory-ladenness that we can learn from the data. In grand philosophical terms, I argue for a rationalist twist to the empiricist orientation of the philosophy of statistics.